Sharp error bounds for some quadrature formulae and applications.
Sharp Estimates in Terms of Moduli of Smoothness for Compound Cubature Rules.
Solving a class of multivariate integration problems via Laplace techniques
We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled...
Some applications and numerical methods for orthogonal polynomials
Some Gauss-Type Formulae for the Evaluation of Cauchy Principal Values of Integrals.
Some new four-point quadrature formulas.
Some new inequalities for means of two arguments.
Some positive Cotes numbers for the Chebyshev weight function.
Some results in multivariate interpolation.
Some results on convergence acceleration for the E-algorithm
Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Spherical quadrature formulas with equally spaced nodes on latitudinal circles.
Spline approximation and generalized Turán quadratures.
Spline quasi-interpolants and quadrature formulas.
Splines in Numerical Integration
AMS Subj. Classification: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the...
Spolehlivost numerických výpočtů
Stable Convergence Acceleration Using Laplace Transforms.
Stochastic Properties of Quadrature Formulas.
Suboptimal Kronrod extension formulae for numerical quadrature.
Sur les formules de quadrature numérique à nombre minimal de noeuds d'intégration.